Variable population exposure and distributed travel speeds in least-cost tsunami evacuation modelling

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Least-cost tsunami evacuation modelling

S. A. Fraser et al.

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Nat. Hazards Earth Syst. Sci. Discuss., 2, 4163–4200, 2014 www.nat-hazards-earth-syst-sci-discuss.net/2/4163/2014/ doi:10.5194/nhessd-2-4163-2014

This discussion paper is/has been under review for the journal Natural Hazards and Earth System Sciences (NHESS). Please refer to the corresponding final paper in NHESS if available.

Variable population exposure and

distributed travel speeds in least-cost

tsunami evacuation modelling

S. A. Fraser1, N. J. Wood2, D. M. Johnston1,3, G. S. Leonard3, P. D. Greening4,

and T. Rossetto4,5

1

GNS Science/Massey University Joint Centre for Disaster Research, Massey University (Wellington Campus), P.O. Box 756, Wellington 6140, New Zealand

2

United States Geological Survey, 2130 SW 5th Avenue, Portland, OR 97201, USA

3

GNS Science, P.O. Box 30 368, Lower Hutt 5010, New Zealand

4

Department of Civil, Environmental and Geomatic Engineering, University College London, Gower Street, London, WC1E 6BT, UK

5

The Earthquake and People Interaction Centre (EPICentre), University College London, Gower Street, London, WC1E 6BT, UK

Received: 23 April 2014 – Accepted: 26 May 2014 – Published: 10 June 2014

Correspondence to: S. A. Fraser ([email protected])

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Abstract

Evacuation of the population from a tsunami hazard zone is vital to reduce life-loss due to inundation. Geospatial least-cost distance modelling provides one approach to as-sessing tsunami evacuation potential. Previous models have generally used two static exposure scenarios and fixed travel speeds to represent population movement. Some 5

analyses have assumed immediate evacuation departure time or assumed a common departure time for all exposed population. In this paper, a method is proposed to in-corporate time-variable exposure, distributed travel speeds, and uncertain evacuation departure time into an existing anisotropic least-cost path distance framework. The model is demonstrated for a case study of local-source tsunami evacuation in Napier 10

City, Hawke’s Bay, New Zealand. There is significant diurnal variation in pedestrian evacuation potential at the suburb-level, although the total number of people unable to evacuate is stable across all scenarios. Whilst some fixed travel speeds can approxi-mate a distributed speed approach, others may overestiapproxi-mate evacuation potential. The impact of evacuation departure time is a significant contributor to total evacuation time. 15

This method improves least-cost modelling of evacuation dynamics for evacuation plan-ning, casualty modelling, and development of emergency response training scenarios.

1 Introduction

Local-source (or near-field) tsunami can cause loss of life due to onshore inundation within minutes after a source event. Prompt evacuation of the hazard zone maximises 20

a person’s chance of surviving tsunami inundation. Well-planned routes and refuges facilitate evacuation by minimising travel time to safety and maximising the number of people reaching safe refuge. Evacuation modelling is an important tool for estimating exposure to the hazard and the time required to evacuate the hazard zone.

Least-cost distance (LCD) analysis is an established method for tsunami evacuation 25

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Riancho et al., 2013; Wood and Schmidtlein, 2012, 2013). LCD analysis is a Geo-graphic Information System (GIS)-based method that computes the minimum cost of travel (generally expended energy or time) between specified source and destination cells in a raster domain (i.e., a cell-based grid). Travel speed values can be applied to the cost distance surface to generate a time surface representing the time to travel from 5

source to destination. Travel time maps enable emergency managers to visualise spa-tial variation in evacuation time (Wood and Schmidtlein, 2012). Comparison of travel time to wave arrival in tsunami inundation scenarios enables identification of areas that cannot be evacuated before wave arrival. Combining travel time and population expo-sure data gives an indication of the number of people potentially unable to evacuate in 10

the available time, which facilitates planning of additional evacuation and emergency response solutions.

In order to simulate evacuation processes at the community scale, a model must represent the physical environment, spatial extent and timing of the hazard, popula-tion exposure, and human behaviour with respect to evacuapopula-tion decisions and timing. 15

To date, LCD models have been tested for sensitivity to elevation and landcover data (Wood and Schmidtlein, 2012). Wood and Schmidtlein (2012) concluded that the use of anisotropic path distance provides a more realistic cost distance estimate than the pre-vious use of isotropic cost distance. Post et al. (2009) applied increased complexity to LCD analysis by including network capacity and evacuee density as modifiers of travel 20

cost. Three other evacuation factors, including population exposure, departure time and travel speed, have not been adequately addressed in terms of their potential variability and have been consistently applied as static values in previous LCD approaches.

The objective of this paper is to demonstrate a method for introducing variability in population exposure scenarios, evacuation departure times and travel speeds into an 25

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aspects have not be incorporated into the demonstrated process. Population-time pro-files are developed to model the distribution of residents and visitors at any time of day, for a weekday or weekend, in any month of the year. Incorporating distributions to model departure time and evacuation travel speed better reflects evacuee behaviour in a real-world evacuation than current GIS-based approaches to mapping evacua-5

tion potential. The ability to model temporally-variable exposure facilitates derivation of hazard exposure, evacuation demands and optimal evacuation routes and refuges for specific scenarios. Emergency managers can use multiple exposure scenarios to develop evacuation training exercises, evacuation planning and casualty estimation.

2 Study area

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To demonstrate the proposed method, we focus on the coastal community of Napier, Hawke’s Bay, New Zealand, which faces a significant local-source subduction zone tsunami hazard (Power, 2013; Fraser et al., 2014). Napier is a coastal city of almost 60 000 people located on largely flat, low-lying topography (Fig. 1a), on the east coast of New Zealand’s North Island. A single numerically simulated inundation scenario 15

is used to demonstrate the proposed evacuation modelling method. The scenario is a tsunami generated by the maximum credibleM_W9.0 local-source earthquake on the Hikurangi subduction zone (Fraser et al., 2014). Simulated wave arrival at shore occurs 38 min after rupture and inundation reaches its maximum extent (>4 km inland) 32 min later. Flow depths exceed 8 m in the first 100 m onshore and generally up to 3 m further 20

than 1 km inland (Fig. 1b). The simulated maximum credible inundation zone is taken to be the tsunami hazard zone and is referred to as such in the rest of this paper.

BluffHill (maximum elevation>100 m) provides the only area of high ground at the coast for refuge, although other areas of high ground exist further inland of the hazard zone (Fig. 1a). The existing building stock is overwhelmingly 1–2 storey light timber 25

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are three storeys or less in height, 40 % of which are light timber construction. The second storey may provide sufficient height for safe refuge in inland areas of the city but this is less likely in the 1 km closest to shore. The probability of moderate to major structural damage due to tsunami loading in the maximum credible tsunami is greater than 80 % for RC and greater than 90 % for timber structures in the maximum credible 5

tsunami (Fraser et al., 2014). Structural assessments are yet to confirm the tsunami-resistance of multi-storey buildings in the city. Therefore, this study does not include any existing buildings as potential refuges when considering pedestrian evacuation potential.

3 Methodology: least-cost path distance approach to determining pedestrian

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evacuation potential

3.1 Anisotropic least-cost path distance analysis

LCD analysis is conducted in ESRI ArcGIS 10.1 following the anisotropic least-cost path distance method of Wood and Schmidtlein (2012). Least-cost path distance de-termines the minimum path distance from every cell in the hazard zone to the nearest 15

point of safety outside the hazard zone. The hazard zone and tsunami arrival time are identified by numerical inundation modelling (Fraser et al., 2014, Fig. 1b). Use of arrival time at shore provides a conservative estimate of arrival time for most locations in the hazard zone because there is additional time before inundation reaches its maximum inland extent.

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The anisotropic approach accounts for the cost associated with direction of travel over sloping terrain of different surface type. High-resolution ground surface Light De-tection and Ranging (LiDAR) data are used to generate a digital elevation model (DEM) at 2 m horizontal resolution. Most short-span bridges in Napier are represented in the LiDAR data but manual augmentation is required to include the deck elevation of longer 25

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intersected by steep terrain, artificially increasing the path distance value on that route. Tobler’s hiking functions (Tobler, 1993) are used to convert directional slope (derived from the DEM) into a travel speed cost, interpreting travel in a downhill direction as a benefit and uphill travel as an additional travel cost.

Land cover data are compiled from aggregated polygon data (Ministry for the Envi-5

ronment, 2009) representing ground surface cover. The aggregated data do not include roads, waterways or buildings, so additional polygon and polyline data are combined into a single comprehensive land cover raster. Land cover is represented in the LCD analysis by using a Speed Conservation Value (SCV), which is a speed-reduction fac-tor representing the ease of travel over that land cover (Wood and Schmidtlein, 2012). 10

Any cell representing a road is assigned SCV₌1.0 (having no impedance on travel speed) and any cell representing a water body or building is defined as impassable, to ensure evacuation routing around these features. Other land cover categories in the study included: Dirt road (SCV₌0.9091), Light brush (0.8333), Heavy brush (0.6667), Hard sand and Swampy bog (both 0.5556).

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3.2 Time-variable population exposure

Estimates of population located within a hazard zone (the exposed population) are required to provide evacuees’ starting locations. Exposure is typically derived directly from census data, which primarily indicates night-time population distributions. Day-time exposure can be estimated by augmenting census data with additional informa-20

tion, such as maximum building capacity determined by floor area (Cousins, 2009), employment records (Wood and Schmidtlein, 2012), or average rates of schooling, em-ployment and numbers of cars at home (Southworth, 1991). In addition to the location of residents who are at home or a workplace, exposure models should include those in institutional facilities, in transit, working outdoors or undertaking leisure activities. Mod-25

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population has been used to represent exposure uncertainty in stochastic agent-based simulations (Mas et al., 2012). Recent progress has been made in modelling population dynamics by assigning population-time profiles to different types of locations (Cockings et al., 2010) and by using transport data in short time-slices to estimate diurnal changes in spatio-temporal population distribution (Kobayashi et al., 2011). However, such time 5

profiles have yet to be applied in tsunami evacuation modelling.

In this study, total night-time population is obtained from 2006 census Usually Res-ident Population (URP) data at meshblock-resolution and adjusted to 2013 values based on local population projections (Statistics New Zealand, 2006, 2012a). A mesh-block is a New Zealand cadastral entity, generally covering less than 1.0–4.4 km2 in 10

Napier (Fig. 1c). Five population groups are defined on the basis of predominant di-urnal activity and age:school/childcare,working-age adults,independent elderly, de-pendent elderly and visitors. The groups are used in the model to assign exposure locations and travel speed distributions. Employment data, education rolls and care facility capacities are used to define the proportion of URP in each population group. 15

Population-time profiles are used to define the certain proportion of each group at different types of location according to the month, day and time of the chosen exposure scenario (Fig. 2). The profiles define three types of location as: home or temporary accommodation (also includes elderly care facilities), work or school/childcare, and unspecified location to represent people in transit or outdoors. Time profiles are devel-20

oped using employment shift patterns (Statistics New Zealand, 2006), regional com-muting patterns1, US diurnal activity patterns (Klepeis et al., 2001), and local knowl-edge of school hours and peak commuting hours. Building locations and occupancy type are obtained from a regional exposure model developed for the national asset and loss model,RiskScape (Cousins, 2009). Two population-time profiles are devel-25

oped for each group, one for a weekday and one for a weekend, to account for differing diurnal activity on working and non-working days. To include seasonal distribution of

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tourists in the exposed population, regional and local monthly visitor data are converted to an average daily number of visitors for each month. A description of the develop-ment of each population group and the respective population-time profile follows in Sects. 3.2.2–3.2.5.

3.2.1 Exposure distribution – methods applicable to all population groups

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The proportion of each population group assigned as being at home is combined into a single “residential population group”. Each meshblock is assigned a residential pop-ulation for that exposure scenario, according to the proportional contribution of the meshblock to total URP. The derived population of each meshblock is then distributed to randomly-selected buildings in that meshblock, in a household group of variable size. 10

Household group size is sampled from a weighted distribution of “number of household occupants”: 36 % of households in Hawke’s Bay comprise two people, 25 % have one person; 15 % have three people and 13 % have four (Statistics New Zealand, 2006). Distribution in a group enables a single travel speed to be assigned to the group, to represent the effect of household evacuation as a group.

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To distribute the proportion of each population group assigned to an unspecified location, a spatially-weighted distribution is developed using a GIS weighted overlay algorithm. In a mixed-density mixed-use urban area, population distribution is unlikely to be entirely random because people spend a significant majority of their time in res-idential buildings (Klepeis et al., 2001; Leech et al., 2002) and are likely to otherwise 20

congregate around commercial services and community facilities. Therefore, building density is used as a proxy to determine the locations of population who are not defined as being at a residence, workplace, school/childcare centre or carehome. Raster sur-faces of (a) commercial-use building density and (b) non-commercial building density are calculated using the Kernel Point Density tool in ArcGIS 10.1. The two surfaces are 25

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weighted cells reflect areas of highest building density, based on building footprint. The population is then distributed according to the weighted surface using a spatial analysis platform (Geospatial Modelling Environment; Beyer, 2012). This approach ensures that while each individual’s location is random, the model contains realistic aggregations of population around commercial and public services and facilities in the city.

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3.2.2 Distribution of working-age adults

Population assigned to a workplace is distributed to randomly-selected commercial, in-dustrial, or community-use buildings until the maximum person-capacity of the building is satisfied. Capacity is determined using the building floor area (m2) and required floor area per person (Cousins, 2009). The proportion of this group assigned to residences 10

and to unspecified locations is distributed according to the method in Sect. 3.2.1. The number of working-age adults (aged 18–65 years) is derived from census data (Statis-tics New Zealand, 2012a). All members of this group are assigned an “adult unim-paired” travel speed.

Employment statistics1 show that approximately 80 % of this group are in employ-15

ment (Napier City Council, 2013). Regional employment shift data show that 89 % of working-age adults are in day-time employment1. Therefore on a weekday, 60 % of working-age adults are assigned to commercial or industrial buildings between 10:00– 16:00, and 20 % to unspecified locations to represent people working in outdoor lo-cations or in transit while working (Fig. 2a). The remaining 20 % are distributed to 20

randomly-selected residential buildings to represent those at home during the day (working and non-working population). In the hours 08:00–10:00 and 16:00–18:00, the proportion of people at unspecified locations peaks to represent commuting between residences and workplaces. There is no data available to inform the rate of movement of people at these times, so the population-time profiles curves are developed with an 25

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commuters. The net balance of commuters is expected to be much less on weekends, so the effect of commuters is only included on weekday. The weekend population-time profile assumes that 40 % of working-age adults are at workplaces during the day, with 40 % at home and 20 % at unspecified locations (Fig. 2b). To account for night-shift workers in buildings, 2.5 % of working-age adults are assigned to workplaces during 5

evening hours and 0.5 % of them are assigned to unspecified locations. The distribu-tion of people working in evenings (8 %) and overnight (3 %) is based on employment shift data1.

3.2.3 Distribution of children to schools and childcare centres

School rolls are obtained for the 34 schools and one tertiary college in Napier (Ministry 10

of Education, 2012a). Attendance rolls for 64 childcare centres are obtained from the Ministry of Education (2012b). Where published roll data are not available for a centre, the mean attendance roll of all other centres is applied. The weekday distribution of children places 100 % of children assumed to be in school or childcare during 09:00– 15:00, and at home during 21:00–07:00 (Fig. 2c). No data are available to inform the 15

distribution of children between school or childcare centre, home and unspecified lo-cations in the intervening hours, so this is subjectively assigned. The combined school and childcare roll (21 200) is greater than the 2013 adjusted population for age group 2–18 yr (13 933). The surplus is assumed to be schoolchildren commuting in from other territorial authorities and they are not included in exposure scenarios between 17:00– 20

07:00.

To account for the total number of people on site, staffnumbers are included in the exposure estimates of childcare facilities using a ratio of one staff member per ten children (Napier Kindergartens, 2012). Sta_ff-to-student ratios are assumed negligible due to the large school population and lower ratio of staffto schoolchildren. All people 25

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3.2.4 Distribution of dependent and independent elderly

The population at 17 elderly care facilities and retirement villages (1000 people) is defined asdependent elderlyand assigned to the slowest travel speed group (elderly). There are an estimated 10 000 people above 65 years who are considered for this analysis to reside at home, defined in this model asindependent elderly. This group 5

are considered to be more mobile than dependent elderly, so are assigned to theadult impairedtravel speed group.

Both groups are part of the non-working population, assumed to be located at home or care facility between 18:00–06:00. Day-time location is assumed to be 60 % at home/facility between 10:00–14:00 and 40 % at unspecified locations. The distribution 10

in the intermediate periods of time (07:00–09:00 and 15:00–17:00) assumes a linear trend to represent travel patterns between home and unspecified locations.

Whilst 65 years (the nominal retirement age in New Zealand) is used in this modelling as a threshold to consider people as non-working, this is arbitrary as a threshold for im-plementing slower evacuation speeds. Assigning a very slow travel speed to everyone 15

above 65 years is unwarranted, as deterioration in mobility is gradual and highly vari-able. Due to the similarity of mean travel speed in the distributions compiled forelderly

andimpaired adults (Fig. 3), application of different minimum-age thresholds (65, 70, 75, 80 and 85 years) for theelderly travel speed causes less than 1 % variation in pop-ulation unable to evacuate before wave arrival. Practically, the two current travel speed 20

distributions could be combined with minimal impact on results, but in order to demon-strate the functionality of the proposed method, both curves are retained in this study. In the absence of empirical data to determine a definitive threshold, the population greater than 80 years has been assigned the elderly travel speed for all subsequent scenario modelling. Improved data on evacuation walking speeds of the elderly, and 25

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3.2.5 Distribution of visitors

The daily number and seasonal variation of overnight and day-trip visitors to Napier are derived from local and regional tourist data (Ministry of Economic Development, 2013a, b; Statistics New Zealand, 2012b, c). Overnight visitors are distinguished by accommo-dation type (commercial or private) and distributed to the appropriate building type in 5

night-time exposure scenarios. Between 23:00–06:00, visitors in private accommoda-tion are distributed in groups of two (mean number of guests per stay night=1.67) to randomly-selected residential buildings in Napier. Those in commercial accommo-dation are distributed in groups of two to randomly selected tourist accommoaccommo-dation (hotel/motel/backpacker/holiday park) according to facility capacity as a proportion of 10

total commercial accommodation capacity. Between 10:00–18:00, 95 % of visitors are distributed to unspecified locations using the spatially-weighted approach, and 5 % are assumed to be at their accommodation. The estimated number of daytrip visitors is dis-tributed with the spatially-weighted random distribution for exposure scenarios between 08:00–20:00.

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3.3 Estimation of evacuation time

A person’s total evacuation time is represented by a series of discrete time components that include event detection, warning transmission and reception, evacuation prepara-tion and evacuaprepara-tion travel (e.g. Urbanik et al., 1980; Post et al., 2009; Purser, 2010; González-Riancho et al., 2013). An evacuation time sequence for an individual or group 20

can be defined as: ETt=EAt+ADt+WDt+IDt+EPt+TTtwhere ETtis total evacuation

time; EAt is time required to detect an event and assess the threat; ADt is authorities’

decision-making time for issuing an advisory/warning after a threat assessment; WD_t is warning dissemination time between the decision to issue a warning and warning receipt by the public; IDt is individual decision-making time on whether to evacuate

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in transit between location at the time of warning and safe destination. An individual is considered to have the potential to evacuate successfully if ETt is less than wave

arrival time.

In local-source tsunami, short wave arrival times and technological limitations mean that the detection and warning phases may not be completed fast enough to provide 5

warning with sufficient time for the subsequent evacuation phases. Instead, tsunami education encourages immediate evacuation on recognition of natural warnings such as earthquake ground shaking or observations of unusual marine phenomena. There-fore, total evacuation time in the case of local-source tsunami is a function of the time for individuals to recognise a threat and decide to evacuate (ID_t), the time it takes them 10

to prepare to evacuate (EP_t), and their travel time (TT_t) so that: ET_t₌ID_t₊EP_t₊TT_t. In this proposed method, evacuation preparation time (Sect. 3.3.1) and travel time (Sect. 3.3.2) are estimated separately and summed to yield total evacuation time for each individual (ET_t). To account for uncertainty in evacuation time for each exposure scenario, 500 simulations of evacuation time are conducted for each individual in the 15

population to generate mean ETt. Individuals whose mean exceeds wave arrival time

are subject to further spatial analysis to calculate the population unable to evacuate the hazard zone before wave arrival (P_VE).P_VE represents the demand for additional evac-uation capacity, such as vertical evacevac-uation refuges in the hazard zone. Evacevac-uation time curves are plotted to show the distribution of population according to evacuation 20

time ETtin 1 min intervals. Figure 4 shows ETtbetween 0–90 min for clarity at the wave

arrival time threshold; the number of people not exposed to tsunami, and those with ET_t>90 min are not shown. The 95 % confidence interval is less than 2 % of the mean population at 20–30 min, and less than 11 % in the tail of the curve (Fig. 4a). The 95 % confidence interval range based on 1000 simulations is less than 1–7 %. Five hundred 25

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3.3.1 Evacuation departure time (IDt+EP_t)

Modelling evacuation departure time is complex and uncertain. Activities in this phase may include gathering possessions, warning/helping others, confirming warnings, seeking additional information, and re-uniting or making contact with family before evacuating together (Drabek, 1986; Lindell and Perry, 1992, 2012). These types of 5

behaviour have been reported in local-source tsunami (Fraser et al., 2012; Yun and Hamada, 2012), but literature concerning tsunami evacuation behaviour remains rel-atively limited (Dash and Gladwin, 2007; Lindell and Prater, 2010). Quantitative data available to constrain tsunami evacuation departure to specific time ranges are limited to very few studies (Suzuki and Imamura, 2005; Mas et al., 2012).

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Substantial numbers of people choose not to, or are unable to evacuate upon re-ceiving hazard warnings (Lindell and Perry, 1992; Johnston et al., 2005; Lindell et al., 2011; Lindell and Perry, 2012), resulting in compliance rate much less than 100 %. Earthquake ground shaking is often not interpreted by people as a tsunami warning (Gregg et al., 2006), therefore not all people evacuate the hazard zone. Compliance 15

rate is little-studied for local-source tsunami, but may be influenced by proximity to the shoreline, property ownership, age and preparation of household plans (Charnkol and Tanaboriboon, 2006; Murakami and Kashiwabara, 2011). Tsunami evacuation intention surveys in our study area suggest relatively high but location-dependent compliance rate based on a natural warning: 84 % for respondents on the street at the time of an 20

earthquake, 56 % when at home (Fraser et al., 2013). A spatially-variable compliance rate is supported in the proposed method but due to the focus on travel speeds in this analysis, compliance rate is assumed to be 100 %.

Preliminary surveys of intended evacuation behaviour among residents and visitors in Napier were unable to quantify evacuation decision-making and preparation time but 25

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rate of increase in the number evacuating, followed by a more rapid rate of evacuation for hurricanes and nuclear accidents (e.g. Tweedie et al., 1986; Lindell et al., 2002; Southworth, 1991). Observed departure times in tsunami events are well-correlated with the Rayleigh function (Imamura et al., 2012; Mas et al., 2012). Suzuki and Ima-mura (2005) estimated that an optimum evacuation curve has a mean value of 7 min, 5

while Mas et al. (2012) proposed that a worst-case curve tends towards arrival time, as people wait until later to evacuate. Following the approach of Mas et al. (2012), Rayleigh curves with mean values of 7 min and 38 min are applied in this analysis as lower and upper bounds potential evacuation-time curves (Fig. 5). For each simulation, a mean departure time value is randomly selected from the range 7–38 min, to gener-10

ate a new Rayleigh function that falls in the shaded area of Fig. 5. Every individual or group is then assigned an evacuation departure time sampled from the corresponding probability density function. Fraser et al. (2013) suggested different intended actions based on gender and location at the time of earthquake, however, in the absence of quantitative data to inform a relationship between the two, departure time is treated as 15

independent of any demographic characteristics or situational/spatial context.

3.3.2 Evacuation travel time (TTt)

Evacuation travel mode, generally pedestrian or vehicular, determines the speed and density at which people can travel through a transport network. Travel mode is influ-enced by distance to destination (Lamb and Walton, 2011), starting location (Fraser 20

et al., 2013), and local context such as regular transportation modes (Murakami and Kashiwabara, 2011; Okumura et al., 2011). Tsunami education promotes pedestrian evacuation in local-source tsunami to minimise traffic congestion that can slow evacu-ation. Previous LCD pedestrian evacuation models have used a single walking speed for all evacuees, or used a different speed for each of several demographic groups, 25

representing the impact of age and relative mobility (Table 1).

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travel speeds to the modelled population, walking speeds identified in the literature are grouped into one of five travel speed groups:Elderly,Child,Adult impaired,Adult unimpaired, andRunning(Table 1). The five travel speed groups are based on the cat-egories given in the originating studies. The travel speeds found in the literature range between 0.21 and 3.83 m s−1

. There is a range of 1.92 m s−1

in the adult unimpaired 5

group, 1.54 m s−1

for children, and 1.09 m s−1

for elderly. These ranges represent vari-ability in walking speeds that has not been captured by previous studies that apply a fixed speed to each category.

The mean speed and standard deviation for each travel speed group (Table 2) are used to generate normal distributions of travel speed (Fig. 3). For each individual, a new 10

travel speed is sampled from the corresponding travel speed distribution in each of the 500 simulations. The inverse of sampled travel speed is multiplied by the least-cost path distance value at the individual’s location, to calculate travel time to safety (TTt).

The proposed method for allocating travel speeds allows for the definition of a prob-ability that an unimpaired adult or child will run in the evacuation, reducing their travel 15

time. The probability of any child or unimpaired adult running is set to 20 %, 40 %, and 60 % in three tests. For each child or unimpaired adult in the exposure model, a ran-domly sampled value between 0–1 determines whether that individual is assigned to therunningtravel speed group, or to their original travel speed group. The proportion of individuals and groups who might run rather than walk in an evacuation is not empir-20

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4 Results

4.1 Spatio-temporal variation in evacuation demand

Twelve exposure scenarios are generated using the time-variable exposure model and analysed for evacuation demand. The scenarios comprised: 02:00 weekday, 12:00 weekday and 12:00 weekend, repeated for February, May and November (high-, low-5

and mid-tourist season, respectively). February weekday 08:00 and 17:00 scenarios, are generated to represent peak commuting times and January weekend 12:00 to demonstrate peak tourist numbers. This range of scenarios demonstrates the flexibility of the time-variable exposure model and assesses the influence of changing exposure on evacuation demand. The results reported in this section use consistent assumptions 10

to demonstrate the influence of exposure changes: 38 min wave arrival time, elderly age threshold of 80 years (Sect. 3.2.4), and 100 % compliance rate.

Total population in each scenario ranges between 92 % of URP for a weekday 17:00 scenario, and 110 % on a weekend at 12:00. The 17:00 scenario omits non-resident school-children and resident (outgoing) commuters, who are assumed to be outside the 15

study area at that time. The weekend 12:00 scenario has a high population because it includes resident commuters and an additional 4000 day-trip visitors. There is sub-stantial diurnal variation in exposure distribution on weekdays. Individual suburbs show population change of −55–150 % when comparing exposure at 02:00 to exposure at

12:00, as residential population is re-distributed to schools and commercial/industrial 20

areas during the day. Variation between suburbs is also significant when comparing weekday and weekend exposure (−54–75 %), but seasonal variation in all suburbs is

relatively limited (generally<11 %).

For this case study, there is some diurnal variation inP_VE(Fig. 4b) but little seasonal variation (Fig. 4c). It is estimated that 15 200–18 800 people (25–30 % of the total pop-25

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end at 12:00 (28–29 %). The weekday 12:00 scenario shows the lowestP_VE(25–26 %). Peak commuting scenarios haveP_VEof 26 % for 08:00 and 29 % for 17:00.

Although absoluteP_VEshows minor fluctuations (5 % of the total population) between each exposure scenario, this masks the significant localised variation inP_VEat suburb level between exposure scenarios (Fig. 6a–c). The darker shades in Fig. 6 indicate 5

high concentrations of P_VE. These locations have the greatest requirement for addi-tional evacuation capacity and could potentially have the highest number of casualties or people trapped in a tsunami. The 02:00 scenario shows a large area of peak P_VE

density in the residential suburbs, which have high concentrations of URP at residen-tial locations overnight.P_VE on a weekday at 12:00 is strongly influenced by the large 10

population concentrations at several schools, which show as two distinct areas of peak density. Otherwise, theP_VE density evident at 02:00 is more evenly distributed in the 12:00 scenario.

MaximumP_VE density occurs in a weekday 02:00 scenario (2800 people km−2_{) and}

is 33–41 % lower for all other scenarios. In the weekend 12:00 scenarios, a smaller 15

proportion of the city has highP_VE density (greater than 1500 people km−2_{) compared}

to weekday 02:00. However, density increases along the coastline and commercial-use areas in weekend day-time scenarios, to a moderate P_VE density of 200– 1000 people km−2_._P

VE in the top three suburbs (in terms ofPVE at 02:00) decreases

in all diurnal comparison scenarios compared to a weekday 02:00. These decreases 20

are on the order of 29–52 % (1000–1900 people). Conversely, other suburbs show in-creases of up to 1600 people (500 %).

It is important to represent the local variation in P_VE and influence of the weekend/peak-commute scenarios to inform appropriate siting choices when plan-ning evacuation. Multiple exposure scenarios can be combined into a maximum ex-25

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12:00 scenarios (i.e. night-time and day-time using employment records) would not, for this study location, accurately represent the maximumP_VE.

In addition to changes in P_VE distribution, composition of P_VE also varies between exposure scenarios. In a weekday 02:00 scenario at Napier, 91 % ofP_VE are people located at home, so the majority of evacuees will be with their household group. At 5

12:00 on a weekday the distribution is more diverse, posing different challenges for evacuation and emergency response than a night-time scenario. Twenty-five percent of the population are at home, 31 % are children at school, 20 % are people at work, and 21 % are tourists, resident adults and elderly people at unspecified locations. In these scenarios, evacuation of large groups becomes more prevalent and immediate actions 10

are likely to include connecting with family and travelling to schools before evacuating. At 12:00 on a weekend,P_VEcomprises 47 % at home, 14 % work, and 31 % of people at unspecified locations (an equal composition of resident adults, children, and tourists). One of the most-vulnerable groups, people in elderly care facilities, comprises<1 % of

P_VE(<200 people) in each scenario. 15

4.2 Evacuation departure time

To demonstrate the importance of including evacuation departure time in evacuation modelling, analysis was conducted with the decision-making and preparation time phases (IDt+EPt) omitted. When evacuation departure time is omitted, in a

Febru-ary 02:00 scenario, ETt is reduced by 15 min on average, reducing PVE from 30 % of

20

total population to 9 %. This represents a reduction of 11 800 people who require addi-tional evacuation capacity (Fig. 4d and 6e). Without evacuation departure time,>50 % of the population have ETt<10 min and several suburbs show no requirement for

addi-tional evacuation capacity. This represents a significant possibility for under-estimating

P_VE and requirements for additional evacuation capacity, reinforcing the need to ade-25

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4.3 Impact of distributed travel speed

The impact of simulating evacuation with distributed travel speeds in a LCD framework has been tested against three fixed travel speeds: 0.89, 1.1 and 1.79 m s−1_{. These}

represent fixed speeds for a mobility impaired adult (FEMA, 2008), unimpaired adult based on US crosswalk standards (Wood and Schmidtlein, 2012), and an unimpaired 5

adult (FEMA, 2008) (Table 1).

The use of fixed speeds can produce comparable results to distributed travel speeds. This is dependent on the fixed speed corresponding with the mean of travel speed distributions. In this case study, a fixed speed of 0.89 m s−1 _{estimates that 37 % of}

the exposed population cannot evacuate in time. Simulation with 1.1 m s−1 _estimates

10

33 % and 1.79 m s−1

estimates 23 %. This compares to 38 % for analysis with dis-tributed travel speeds. This corresponds to a P_VE range of 4600 people across the three fixed speed estimates, which is a significant variation in the estimate of required additional evacuation capacity. The use of 1.1 m s−1

provides a reasonable assumption to estimate total P_VE where travel speed distributions cannot be modelled (Fig. 4g). 15

However, the 1.1 m s−1 _{fixed speed curve results in a greater number of people with}

ET_t of 38–80 min than a distributed speed analysis, which contains more people with ETt>90 min. Therefore, PVE is more sensitive to changes in evacuation time when

a fixed speed of 1.1 m s−1 _{is used. If this fixed speed is used to assess the impact of}

education to reduce evacuation delays, it is likely to show greater reductions in evacua-20

tion demand than analyses with distributed speed. A fixed speed of 0.89 m s−1

provides a conservative estimate ofP_VE, which is generally desirable for evacuation planning, but is less suitable for estimating evacuation demand when designing evacuation refuge capacity and informing investment decisions. A fixed speed of 1.79 m s−1

underesti-matesP_VE compared to the distributed speed approach.

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safety zone, because a small change in travel speed determines whether ET_t exceeds wave arrival time or not. Distribution of P_VE density for a fixed speed of 0.89 m s−1

corresponds closely to that of the distributed speed analysis, although the extent of high density (>1500 people km2) is greater than for distributed speeds (Fig. 6f). At 1.1 m s−1_,

the spatial extent of high density begins to reduce, with no reduction in peakP_VEdensity 5

(Fig. 6g). For 1.79 m s−1

several suburbs are estimated to have no requirement for additional evacuation capacity (Fig. 6h); use of this speed could lead to locations that require vertical evacuation being overlooked in decision-making processes.

4.4 Application of running speeds

The proposed method enables application of faster travel speeds to proportions of 10

unimpaired adults or children, to test the effect on P_VE of the probability that people may run to evacuate. In three di_fferent tests, probability of an unimpaired adult or child being assigned a travel speed sampled from theRunning speed distribution (Fig. 3) is set to 20, 40 and 60 %. With a 20 % probability of running,P_VE is reduced by 6 %. A 12 % decrease in P_VE is achieved with 40 % probability and 17 % reduction with 15

a 60 % probability (Fig. 4f). These results show the tangible impact (reduction in number of casualties) that is possible due to an increase in travel speeds, and demonstrates the utility of this method in testing the impact of faster evacuation due to education and evacuation training. This approach could also be used to quantify the potential benefits of increased bicycle use in evacuations, to determine whether it is worthwhile trying to 20

increase the use of bicycles in evacuation.

5 Conclusions

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to provide exposure distributions for several population groups for any month, day or time. A Rayleigh function is applied to account for uncertain evacuation departure time. A review of pedestrian evacuation models shows that a wide range of travel speeds have been applied as one or several fixed speeds in previous analyses. It is postulated that this is not representative of natural variability in pedestrian travel speeds of a pop-5

ulation. Previously-used travel speeds are collated into travel speed distributions for different population groups based on age and relative mobility.

Modelling multiple exposure scenarios facilitates visualisation of the temporal dimen-sion, in addition to spatial distribution, of evacuation demand. This enables emergency managers and planners to understand how the time of an event can affect hazard ex-10

posure and potential casualties. Pre-calculatedP_VE maps and statistics, derived from a large enough range of exposure scenarios, could assist in: real-time decision-making to expedite emergency response to areas with greatestP_VE; casualty estimation; public education; and evacuation planning. Robust evacuation planning requires knowledge of maximum potentialP_VE at any location to ensure that routes and refuges have suffi -15

cient capacity in any event.

In this case study location,P_VEvaries little due to diurnal changes in exposure, how-ever, significant temporal variations in P_VE are apparent when comparing individual suburbs. A typical analysis using two-scenarios (day-time/night-time) has the potential to overlook the full range of diurnal variation in evacuation demand, particularly in ar-20

eas that have large exposure of transitional populations at peak commuting times and on weekends. Seasonal variation is found to be less important for this case study but should not be ruled out for other locations with a higher ratio of visitors to residents. Maximum potentialP_VEcan be calculated in a single ETtanalysis, but the estimation of

maximum exposure should be based on multiple exposure scenarios, including peak 25

commuting hours and weekends, rather than just two scenarios covering night-time and day-time.

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and internationally. There remains some disparity in diurnal patterns between the population-time profiles developed for this study and those determined from large sam-ples in the US and Canada. The improvement of diurnal activity data and temporally-variable exposure datasets would benefit future risk assessments and evacuation mod-elling for all hazards. This analysis applied 500 simulations of evacuation time to a pop-5

ulation distribution that was unchanged in each exposure scenario. Future analyses should aim to use probabilistic exposure distribution in each simulation to better repre-sent uncertainty in exposure.

Results of evacuation modelling are highly sensitive to the travel speeds applied. The use of fixed speeds∼1.1 m s−1 results in PVE consistent with distributed speeds.

10

However, the slowest speeds used in previous analyses would over-estimate evacu-ation demand, and the fastest would significantly under-estimate demand. There is a requirement to constrain travel speeds in community-scale evacuations. Collection of travel speed data for a range of demographic groups in monitored evacuation exercises could improve distributed travel speed models. This is particularly important for schools 15

and other institutions where group dynamics are likely to affect evacuation speeds. There are currently insufficient data on the time required to conduct preparation activ-ities, to quantify preparation time according to personal characteristics and situational context. Quantification of departure time according to different preparation activities would benefit evacuation modelling and planning, and enable validation of Rayleigh 20

functions. It has been demonstrated that a reduction in departure time can significantly reduce evacuation time and increase the proportion of the population able to reach safety. It is important that models incorporate departure time, and that reduction of this phase is a central aim of tsunami education.

Finally, the proposed method provides spatio-temporal variation in evacuation de-25

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one part of a robust evacuation plan. Complementary agent-based evacuation simu-lation should be used to validate the results of this least cost distance method and to elaborate on traffic modelling, network capacity issues and evacuee interactions. The potential disruption to evacuation routes, damage to buildings and infrastructure as a result of earthquake ground shaking, and the effect of aftershocks on evacuation 5

should be considered in future analyses.

Acknowledgements. This research was supported by public research funding from the Govern-ment of New Zealand and the US Geological Survey (USGS) Land Change Science Program. We would like to thank Jim Cousins (GNS Science) for valuable discussion of exposure mod-els; Megan Harris (Hawke’s Bay Tourism) for provision of tourism data; Lisa Pearse (Hawke’s

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Bay Civil Defence Emergency Management Group) and Craig Goodier (Hawke’s Bay Regional Council) for provision of topography data; Robyn Tuohy (Massey University) for discussion of age-dependent mobility; and Jeanne Jones (USGS) for providing information on application of ArcGIS anisotropic least-cost path distance module. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the US Government.

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Ministry of Education: Directory of Schools – as at 01/08/2012, available at: http://www.minedu. govt.nz/Parents/AllAges/SchoolSearch.aspx (last access: 8 October 2013), 2012a. 4172 Ministry of Education: Early Childhood Education (ECE) Services Listing (updated at 28

September 2012), available at: http://www.minedu.govt.nz/Parents/AllAges/ECEListing.aspx

30

(last access: 8 October 2013), 2012b. 4172